ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60, 86, 94 Yadrenko, Mikhail, Kyiv University, Ukraine Extrapolation and filtering problems for isotropic random fields Let (ξ(x), η(x)) be a homogeneous and isotropic random field on R^{n} and let observations of the field ξ(x) on the sphere S_{n}(r) = {x : |x| = r} be known. An algorithm is proposed for construction of the linear least square estimate η̂(y) of the value η(y) for y ∈ R^{n}. The problem of optimality of the region of observations is discussed. The extrapolation problem is considered for random fields ξ(x) which satisfy the equation (∇^{2} − c^{2})ξ = w where w is a white noise on R^{n}. Reference: M. Yadrenko, Spectral Theory of Random Fields, Opt. Software Inc., N. Y. (1983).